Singularity exponent from wavelet-based multiscale analysis: A new seismic attribute

Seismic interpretation has been traditionally based on reflections or amplitudes. However, amplitude alone can also disguise the true nature of subsurface geology and blur stratigraphic boundaries. In many cases important information is carried by singularities that are not necessarily associated to certain amplitude patterns. We present Hölder exponent (α) as a new seismic attribute which captures the locations and strengths of irregularities in the data. Hölder exponent (α) is a measure of singularity strength defined at or around a point. Higher α indicates higher degree of regularity, and vice versa. It is demonstrated that α is a natural attribute for delineating stratigraphy boundaries due to its excellent abilities in detecting detailed geologic features from seismic data. We test our concept and wavelet-based multiscale analyzing algorithm on both synthetic and seismic data, and show that α improves our ability in the delineation of stratigraphy layers that would be otherwise vague in the original seismic amplitude display.